Linear Programming and systems of inequalities

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Tags

CCSS.HSA.REI.D.12

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Tags

CCSS.HSA.REI.D.12

• (0, 0), (0, 6),
  (6, 2), (8, 0)
• (0, 0), (6, 0),
  (2, 6), (0, 8)

Tags

CCSS.HSA.REI.D.12

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). Which expression can be used to determine the cost (this is called the objective quantity)?

• 30x + 50y

• 50x + 30y

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.1

Which point below when substituted into the expressions gives the most profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.12

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

How many of each purse should Sarah make to maximize profit?

• 6 big purses
• 8 small purses
• 6 small purses and 2 big purses

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.C.6

Objective quantity:
30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300
• 280
• 400
• 240

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2
• y < 2x - 4
  y < 2
• y > 2x - 4
  y <  2 
• y < 2x - 4
  y <   -2

Tags

CCSS.HSA.REI.D.12